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Finding the shortest ladder

  1. Oct 8, 2008 #1
    Finding the "shortest ladder"

    Problem

    I was given an analogy involving a ladder that goes over a fence and then leans against a wall a meter after the fence. The question wanted me to answer "what is the shortest ladder that goes over the fence and reaches the wall"


    3. The attempt at a solution

    I worked out the equation of the "ladder" (i.e line from the ground to the wall) is:

    (3sqrt(3) / sin x) + sec x

    (where x is the angle the ladder makes with the ground and the wall)

    How can i work out the "shortest" ladder that can be made to reach the wall. Is is simply the derivative of the ladder?
     
    Last edited: Oct 8, 2008
  2. jcsd
  3. Oct 8, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    Re: Finding the "shortest ladder"

    So 3sqrt(3) must be the height of the ladder h, right? Yes, the length of the ladder is L=h/sin(x)+1/cos(x). Differentiate that with respect to the angle, x, set it equal to zero and solve for x.
     
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